A response surface method-based hybrid optimizer

Economic competitiveness is driving industry to new frontiers of engineering design. Robustness and reliability based design, multidisciplinary simulation based design, increased complexity and sophistication of our design, and optimization aided design are four such areas, which are seriously challenging our ability to keep pace with the need to adequately model the systems we seek to design – in spite of the exponential growth of computing power. An emerging consensus within the community is that the effective development of computationally benign models (metamodels) will help us navigate the challenging road ahead. The process of constructing metamodels for computationally expensive models, such as finite element, aerodynamic, and heat transfer models, is representative of the tasks we must address. Among the available metamodeling techniques, Radial Basis Functions (RBFs) have recently generated much interest for their effectiveness and versatility. Radial basis functions offer numerous advantages over traditional the Response Surface Methodology (RSM), including their ability to effectively generate multidimensional interpolative approximations. This paper, however, shows how the typical RBF approach lacks the critical flexibility required to handle the wide variety of complex models arising from the use of advanced techniques, such as uncertainty handling and multiobjective optimization, often encountered in modern design. Further, in this paper, we propose a powerful new approach – the Extended Radial Basis Function (E-RBF) approach – that provides the designer with significant flexibility and freedom in the metamodeling process, compared to conventional RBFs. Examples are provided that demonstrate the effectiveness of the new approach, and explore its potential superiority over traditional RBF and response surface methodologies. Initial investigation indicates that the E-RBF possesses unique and novel properties not available in any other single method.

The method of radial basis functions (RBFs) is a method of scattered data interpolation that has many applications in different fields. Based on the RBFs approach, two simple and accurate methods are presented in this paper to favor the solution of fractional optimal control problems (FOCPs) which are nominated as indirect and direct methods. In the first one, the considered FOCP is converted into a system of fractional differential equations (FDEs) that is called two-point boundary value problem (TPBVP) of fractional order. Then, both the context of minimization the total error and a joint application of Volterra integral equation will be used to rewrite this problems as as an unconstrained optimization problem that can be solved by using RBFs approximation. In direct one, we rewrite the FOCP as a classical static optimization problem that can be easily solved using known formulas for computing fractional derivatives of RBFs. Numerical example are given to prove the accuracy, effectiveness and feasibility of these methods.

This research investigated and optimized the separation of carbon dioxide (CO2) from natural gas in an adsorption column filled with grafted-beam nanofiber adsorbent. The main purpose of using ANN and RSM models in this manuscript is to compare these two methods in predicting the CO2 adsorption capacity. In other words, it was made to find a suitable model that has the highest agreement with the experimental data. Also, the other purpose of using the RSM model is to detect the optimized empirical conditions. Moreover, two common ANN models are applied in this work, including a multilayer perceptron (MLP) and radial basis function (RBF). The novelties of this work are explained as follows: (1) detecting the optimized synthesis factors of NF-PAN/PUGMA sorbent which possess the highest CO2 adsorption capacity with the help of response surface methodology (RSM), (2) studying the simultaneous interaction of synthesis parameters on the CO2 adsorption capacity with the help of both RSM and artificial neural networks (ANNs), (3) testing two types of ANN models including multilayer perceptron (MLP) and radial basis function (RBF) to predict the effect of monomer volume percentage and irradiation dose on the CO2 adsorption capacity. Indeed, finding the best model (ANN or RSM) can help engineers in practical applications predict CO2 adsorption capacity using NF-PAN/PUGMA under different conditions without incurring high-priced chemical materials, electricity, or human resources. The validation results were examined using correlation coefficients (R2) of RSM, RBF, and MLP models. The correlation coefficients for the RSM, RBF, and MLP models were 0.9910, 0.9949, and 0.9968, respectively. Additionally, the average absolute relative deviation (AARD) values for the RBF and MLP models were 0.00046512 and 0.00045511, respectively, indicating that the MLP model is better than the RBF model. To identify the optimal network structure, the trial-and-error method was conducted for MLP and RBF models. The number of neurons was found at 12 and 45 for MLP and RBF, respectively. The optimized effective parameters were obtained using RSM: 25.80% GMA, 66.45% amine, and an irradiation intensity of 28kGy.

This paper discusses the influence of different Radial Basis Function (RBF) in metamodel construction to be applied to 3D aerodynamic wing optimization problems using the Constrained Optimization with Response Surface (CORS) methodology in conjunction with a stochastic Controlled Random Search Algorithm (CRSA). CORS methodology is based on the iterative construction and optimization of response surfaces with a robust search pattern application. In the CORS methodology the response surface may be generate by at least three types of methods: (i) Classical (polynomials and parametric surfaces), (ii) Statistical (K-Nearest, Kriging and Gaussian Processes) and (iii) Advanced (RBF and Neural Network). The response surfaces used in this paper are constructed using six different types of RBF: Gaussian, Hardy’s Multiquadric and Inverse Multiquadric, which depend on a shape parameter, and linear, cubic and thin plate spline, which do not depend on a shape parameter. The RBF’s are directly applied on the response surface construction inside the CORS structure. Thus the choice of a RBF and of a shape parameter (being the case) may influence significantly the methodology efficiency. The CORS methodology is here applied for accelerating the optimization process of wing aerodynamic designs with a solver based on a first order 3D panel method and a 2D boundary layer model. Since the main objective of this paper is of prospective nature, the choice of a relatively low-fidelity flow computation solver is justified. One considers problems of minimizing the aerodynamic coefficient relation (CD/CL) and the inverse of lift coefficient (1/CL). Comparative influence of the RBF choice on the acceleration induced by CORS methodology is investigated taking into account the number of expensive objective function evaluations necessary to find the minimum value in each problem.

This paper presents a new method to construct response surface function and a new hybrid optimization method. For the response surface function, the radial basis function is used for a zeroth-order approximation, while new bases is proposed for the moving least squares method for a first-order approximation. For the new hybrid optimization method, the gradient-based algorithm and pattern search algorithm are integrated for robust and efficient optimization process. These methods are based on: (1) multi-point approximations of the objective and constraint functions; (2) a multi-quadric radial basis function for the zeroth-order function representation or radial basis function plus polynomial based moving least squares approximation for the first-order function approximation; and (3) a pattern search algorithm to impose a descent condition. Several numerical examples are presented to illustrate the accuracy and computational efficiency of the proposed method for both function approximation and design optimization. The examples for function approximation indicate that the multi-quadric radial basis function and the proposed radial basis function plus polynomial based moving least squares method can yield accurate estimates of arbitrary multivariate functions. Results also show that the hybrid method developed provides efficient and convergent solutions to both mathematical and structural optimization problems.

Dengue fever is an arbovirus disease caused by dengue virus infection through the bite of the Aedes mosquito, Aedes aegypti. Signs or symptoms of dengue usually resemble ordinary viral infections, but can become more severe and cause other symptoms that can paralyze the activities of the patient who suffers from it. The initial symptoms of someone who is infected with the dengue virus will experience a fever within 4–6 days after being infected. Therefore, early diagnosis is needed whether a person is infected or not with dengue fever. Because if someone is late getting treatment by medical personnel, then this can lead to death. Prevention can be done by making the right predictions. Dengue fever disease prediction research is needed to assist medical personnel in making a diagnosis. To get a good level of accuracy, research collected data and used the Radial Basis Function (RBF) approach method. The results of the RBF prediction evaluation obtained are that the RBF model gets 100% accuracy, 100% sensitivity, 100% specificity, and 100% AUC value.

This study evaluates the effectiveness of Radial Basis Function (RBF) approaches, specifically Gaussian and Multiquadric RBFs, compared to Cubic and Adaptive Splines for data imputation in time-series datasets. Three datasets—multi-seasonal, non-stationary, and spikes and drops—were used, with varying data corruption levels to simulate real-world scenarios. Imputation performance was assessed using Root Mean Square Error (RMSE). The results indicate that spline-based methods, particularly Cubic and Adaptive Splines, consistently deliver lower RMSE values, showcasing superior robustness to data variability and high corruption levels compared to RBF methods. This comparative analysis offers insights into selecting appropriate techniques for effective data imputation in time-series analysis.

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When radial basis functions (RBFs) are made increasingly flat, the interpolation error typically decreases steadily until some point when Runge-type oscillations either halt or reverse this trend. Because the most obvious method to calculate an RBF interpolant becomes a numerically unstable algorithm for a stable problem in the case of near-flat basis functions, there will typically also be a separate point at which disastrous ill-conditioning enters. We introduce here a new method, RBF-QR, which entirely eliminates such ill-conditioning, and we apply it in the special case when the data points are distributed over the surface of a sphere. This algorithm works even for thousands of node points, and it allows the RBF shape parameter to be optimized without the limitations imposed by stability concerns. Since interpolation in the flat RBF limit on a sphere is found to coincide with spherical harmonics interpolation, new insights are gained as to why the RBF approach (with nonflat basis functions) often is the more accurate of the two methods.

In this paper, a fractional order digital differentiator is designed by using Inverse multiquadric radial basis function (RBF). First, the RBF interpolation approach is described. Then, the non-integer delay sample estimation is derived by using RBF approach. Next, the Grunwald-Letnikov derivative and non-integer delay sample delay are applied to obtain the transfer function of the proposed method i.e. fractional order digital differentiator. The design accuracy of the proposed method is better then the conventional methods like examples Time domain least squares method, Fractional sample delay method and Frequency response approximation method.

Dynamic frequency scaling (DFS) is one of the most important approaches to saving power in modern day processors. With ever-increasing complexity at system, circuit and device levels, the problem of achieving an efficient DFS boils down to multi-parametric nonlinear optimization. Therefore, it is imperative to explore ingenuous approaches to DFS which could identify an optimal underclocking frequency on-the-fly using an adaptive mechanism. This paper proposes an offline neural network approach to DFS of a ubiquitous single-core processor where several performance parameters of the processor were monitored under application of a number of clocking frequencies. The dataset thus generated was used to train two classifiers, viz. the radial basis function network and the probabilistic neural network. Under changing parametric conditions of the proposed network, the model was fit to performance-monitoring data while running 64-point and 1024-point FFT applications, and one benchmark application named basicmath. To demonstrate the generalization of the classifiers, the models were trained offline by the dataset obtained by clubbing the aforementioned applications. The performance of both the classifiers was found to be promising, and good generalization was obtained with all the datasets. The results indicate toward suitability of trained radial basis family of networks for on-chip deployment for implementing on-the-fly DFS.

A hybrid method for robust and efficient optimization process is developed by integrating a new response surface method and pattern search algorithm. The method is based on: (1) multipoint approximations of the objective and constraint functions, (2) a multiquadric radial basis function (RBF) for the zeroth-order function approximation and a new RBF plus polynomial-based moving least-squares approximation for the first-order enhanced function approximation, and (3) a pattern search algorithm to impose a descent condition and applied adaptive subregion management strategy. Several numerical examples are presented to illustrate accuracy and computational efficiency of the proposed method for both function approximation and design optimization. To demonstrate the effectiveness of the proposed hybrid method, it is applied to obtain optimum designs of a microelectronic packaging system. A two-stage optimization approach is proposed for the design optimization. The material properties of microelectronic packaging system and the shape parameters of solder ball are selected as design variables. Through design optimization, significant improvements of durability performances are obtained using the proposed hybrid optimization method.

The prediction accuracy and applicability of the radial basis function(RBF) and the response surface method(RSM) are studied, and an optimization idea is put forward to solve the problem of selecting an applicable shaping parameter of the RBF model when the surrogate model technology is employed in structure crashworthiness optimization. The genetic algorithm(GA) is used to optimize the crashing energy absorption of a thin-walled structure and find the global optimum which can be viewed as the target of the surrogate model. The necessity of testing surrogate model's prediction accuracy via numerical examples is demonstrated and the applicability of several methods of design of experiments is tested. Thaping parameter of RBF model is treated as a variable, and a few random sample points are used to update radial basis function model suitable. The results show that the updated radial basis function model will be more suitable for structure crashworthiness problem.

This study investigates the properties of SnO2 nanomaterials as CO2 adsorbents. Although CO2 capture technologies have significantly advanced, challenges such as high costs and limited scalability persist. In recent years, nanomaterials have emerged as promising candidates for CO2 adsorption due to their high adsorption capacity, lower cost, and wide availability. However, future research should focus on developing low-cost and efficient nanomaterials to enable large-scale industrial CO2 capture. This study examined the CO2 adsorption capacity using SnO2 nanoadsorbents by employing response surface methodology (RSM) and artificial neural networks (ANNs), specifically radial basis function (RBF) and multilayer perceptron (MLP) networks, for process modeling and optimization. Through the analysis of experimental data, temperature, pressure, and adsorption time were identified as crucial influencing factors. The R2 value of 0.9933 for RSM indicated a great match, whereas the R2 value of one for ANNs indicated superior predictive accuracy. With a minimum mean squared error (MSE) of 0.00012 for the dataset, the MLP was trained using a three-layer activation function. With 288 neurons and a spread of 2, the RBF network achieved an R2 value of 0.9985 and a minimal MSE of 0.00075. The smooth MLP plots effectively captured complex discontinuities, showcasing the superior predictive abilities of ANNs for optimizing the CO2 adsorption process using SnO2 nanoadsorbents, while the RSM surfaces exhibited rigid, polynomial-based patterns.

In many technical applications, reconstruction of the scattered data is often task. For big scattered dataset in n-dimensional space, the using some meshless method such as the radial basis function (RBF) approximation is appropriate. RBF approximation is based on the distance computation, and therefore, it is dimensionally non-separable. This approximation can be converted to an overdetermined linear system of equations which has to be solved.